CPM – Critical Path Method In 1957, DuPont developed a project management method designed to address the challenge of shutting down chemical plants for maintenance and then restarting the plants once the maintenance had been completed. Given the complexity of the process, they developed the Critical Path Method (CPM) for managing such projects. CPM provides the following benefits: Provides a graphical view of the project. Predicts the time required to complete the project. Shows which activities are critical to maintaining the schedule and which are not. CPM models the activities and events of a project as a network. Activities are depicted as nodes on the network and events that signify the beginning or ending of activities are depicted as arcs or lines between the nodes. The following is an example of a CPM network diagram: CPM Diagram [pic] Steps in CPM Project Planning Specify the individual activities. Determine the sequence of those activities. Draw a network diagram. Estimate the completion time for each activity. Identify the critical path (longest path through the network) Update the CPM diagram as the project progresses. . Specify the Individual Activities From the work breakdown structure, a listing can be made of all the activities in the project. This listing can be used as the basis for adding sequence and duration information in later steps. 2. Determine the Sequence of the Activities Some activities are dependent on the completion of others. A listing of the immediate predecessors of each activity is useful for constructing the CPM network diagram. 3. Draw the Network Diagram Once the activities and their sequencing have been defined, the CPM diagram can be drawn. CPM originally was developed as an activity on node (AON) network, but some project planners prefer to specify the activities on the arcs. 4. Estimate Activity Times Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used. A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion times. For each activity, the model usually includes three time estimates: Optimistic time – generally the shortest time in which the activity can be completed. It is common practice to specify optimistic times to be three standard deviations from the mean so that there is approximately a 1% chance that the activity will be completed within the optimistic time. Most likely time – the completion time having the highest probability. Note that this time is different from the expected time. Pessimistic time – the longest time that an activity might require. Three standard deviations from the mean is commonly used for the pessimistic time. PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time for each activity can be approximated using the following weighted average: Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6 This expected time may be displayed on the network diagram. To calculate the variance for each activity completion time, if three standard deviation times were selected for the optimistic and pessimistic times, then there are six standard deviations between them, so the variance is given by: [ ( Pessimistic – Optimistic ) / 6 ]2 5. Identify the Critical Path The critical path is the longest-duration path through the network. The significance of the critical path is that the activities that lie on it cannot be delayed without delaying the project. Because of its impact on the entire project, critical path analysis is an important aspect of project planning. The critical path can be identified by determining the following four parameters for each activity: ES – earliest start time: the earliest time at which the activity can start given that its precedent activities must be completed first. EF – earliest finish time, equal to the earliest start time for the activity plus the time required to complete the activity. LF – latest finish time: the latest time at which the activity can be completed without delaying the project. LS – latest start time, equal to the latest finish time minus the time required to complete the activity. The slack time for an activity is the time between its earliest and latest start time, or between its earliest and latest finish time. Slack is the amount of time that an activity can be delayed past its earliest start or earliest finish without delaying the project. The critical path is the path through the project network in which none of the activities have slack, that is, the path for which ES=LS and EF=LF for all activities in the path. A delay in the critical path delays the project. Similarly, to accelerate the project it is necessary to reduce the total time required for the activities in the critical path. 6. Update CPM Diagram As the project progresses, the actual task completion times will be known and the network diagram can be updated to include this information. A new critical path may emerge, and structural changes may be made in the network if project requirements change. CPM Limitations CPM was developed for complex but fairly routine projects with minimal uncertainty in the project completion times. For less routine projects there is more uncertainty in the completion times, and this uncertainty limits the usefulness of the deterministic CPM model. An alternative to CPM is the PERT project planning model, which allows a range of durations to be specified for each activity.